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A calibration form on a Riemannian manifold M is a differential p-form phi such that 1. phi is a closed form. 2. The comass of phi, sup_(v in ^ ^pTM, |v|=1)|phi(v)| (1) ...

A coordinate system (mu,nu,psi) defined by the coordinate transformation x = (munu)/((mu^2+nu^2)^2)cospsi (1) y = (munu)/((mu^2+nu^2)^2)sinpsi (2) z = ...

According to Pólya, the Cartesian pattern is the resolution method for arithmetical or geometrical problems based on equations. The first step is to translate the question ...

Inscribe a triangle in a circle such that the sides of the triangle pass through three given points A, B, and C.

A minimal surface given by the parametric equations x(u,v) = u-sinucoshv (1) y(u,v) = 1-cosucoshv (2) z(u,v) = 4sin(1/2u)sinh(1/2v) (3) (Gray 1997), or x(r,phi) = ...

If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the ...

A special point which usually has some symmetric placement with respect to points on a curve or in a solid. The center of a circle is equidistant from all points on the ...

An Cesàro equation is a natural equation which expresses a curve in terms of its arc length function s(t) and radius of curvature rho(t) (or equivalently, the curvature ...

A chamfered cube, also inaccurately called a truncated rhombic dodecahedron or more accurately called a tetratruncated rhombic dodecahedron, is a polyhedron obtained by ...

A chamfered dodecahedron, inaccurately called a truncated rhombic triacontahedron or more accurately called a pentatruncated rhombic triacontahedron, is a polyhedron obtained ...